In relation to "identifying problems," the difference between PMs and general employees (those who have to use the software systems and live with the products) at a company is...
1. Good product judgment, taste, and perspective
2. Principled prioritization
3. Detailed requirements analysis
4. Methodical execution until solved
If you want to switch to PM, you need to get past the general sense of "there are problems everywhere" and get to specificity and clarity until problems are solved - one by one.